Using Generalized Poisson Distribution to Model the Patterns of Species Abundances in Three Layers of South Subtropical Forest

doi:10.16258/j.cnki.1674-5906.2022.01.003

Ecology and Environment ›› 2022, Vol. 31 ›› Issue (1): 17-25.DOI: 10.16258/j.cnki.1674-5906.2022.01.003

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Using Generalized Poisson Distribution to Model the Patterns of Species Abundances in Three Layers of South Subtropical Forest

YIN Zuoyun¹^,²^,³()

1. College of Horticulture and Landscape Architecture, Zhongkai University of Agriculture and Engineering, Guangzhou 510230, P. R. China
2. Guangdong Forest Research Institute (Guangdong Academy of Forestry), Guangzhou 510520, P. R. China
3. South China Botanical Garden of the Chinese Academy of Sciences, Guangzhou 510650, P. R. China

Received:2021-08-13 Online:2022-01-18 Published:2022-03-10
Supported by:
Provincial Major Project of Education Department of Guangdong Province, China(2016KZDXM002)

南亚热带森林3层次物种多度之广义泊松分布模型

殷祚云¹^,²^,³()

1.仲恺农业工程学院园艺园林学院,广东广州 510230
2.广东省林业科学研究院,广东广州510520
3.中国科学院华南植物园,广东广州 510650

Abstract

Abstract:

The species abundance distribution (SAD) in a biological community showed typical inverse J-shaped pattern, and the SAD modelling study was contributed to solve practical problems such as the species configuration in forest ecological restoration. This study examines whether a discrete distribution with over-dispersion (i.e., variance>mean), the generalized Poisson (GP) distribution with two parameters, λ and α, can describe the SAD pattern, and whether its parameters are related to community species diversity by using the data from the three layers of a lower subtropical mixture forest in Dinghushan Biosphere Reserve, South China. The results showed that the observed SADs for all three layers of the forest showed similar inverse J-shaped distribution curves and followed the zero-truncated GP, with significantly decreasing λ and slightly increasing α from the tree, shrub to herb layer in the community. The parameter α better reflected the species diversity than λ, and thus the former could serve as a measure of the species diversity in a community. Comparisons between the GP and the Poisson lognormal (PLN) distribution showed that the former better fitted the SAD datasets than the latter for three layers. Therefore, the GP better estimated the potential species richness in the community. The GP distribution was more suitable to model the observed SAD with over-dispersed count data than the PLN, and thus the former might have a wider application prospect than the latter, especially in the estimation of the potential species richness in a community as well as on a local or regional scale and the determination of the species proportion for ecological restoration of degraded forests.

Key words: species abundance distribution (SAD), generalized Poisson distribution, Poisson lognormal distribution, forest layers, maximum likelihood method

摘要：

生物群落中物种多度分布（species abundance distribution）呈典型的倒J形,即其中存在许多稀有种、少量常见种。物种多度分布模型研究有助于解决森林生态恢复中的物种配置等实际问题。本研究考察了一种过分散（over-dispersion,或称超分布,即方差大于均值）的离散型分布,即具有λ和α两个参数的广义泊松（generalized Poisson,GP）分布,能否描述群落中物种多度格局,其参数是否与物种多样性有关。以位于华南地区的鼎湖山生物圈保护区中南亚热带针阔叶混交林为研究对象,利用此群落中乔木层、灌木层和草本层3个层次的物种多度数据,进行了模型拟合与对比研究。采用最大或然法和试值法,在数学工具软件Mathematica 4中编制计算程序,完成分布模型参数的估计;采用卡方检验法考察模型对数据的适合度,再运用Akaike信息准则（AIC）和一致性Akaike信息准则（CAIC）对不同模型间的适合性进行比较。结果表明：（1）本森林群落中乔木层、灌木层和草本层全部3个层次的实测物种多度分布图都呈现相似的倒J形曲线,在统计学上均可用零截断的广义泊松分布进行较好地拟合;（2）从乔木层、灌木层到草本层,λ显著增加,而α则略有减少,且后者的变化趋势与Shannon-Wiener多样性指数和均匀性指数一致,表明参数α可作为群落中物种多样性的量度;（3）通过广义泊松分布和泊松对数正态（Poisson lognormal,PLN）分布的模拟比较可知,前者更适合定量描述群落3层次的物种多度数据,从而能更好地估计出本群落潜在的物种丰富度。群落中全部物种多度的超分布与其每个组成物种种群的超分布（即在空间上呈现聚集分布格局）有关。由于广义泊松分布模型比泊松对数正态分布模型更适合仿真过分散分布的实测物种多度计数数据,因而前者的应用前景可能比后者更广泛,特别是用于估计森林群落中（乃至在当地和区域尺度上）的潜在物种丰富度以及确定退化森林生态恢复的物种配置比例。

关键词: 物种多度分布, 广义泊松分布, 泊松对数正态分布, 森林层次, 最大或然法

CLC Number:

YIN Zuoyun. Using Generalized Poisson Distribution to Model the Patterns of Species Abundances in Three Layers of South Subtropical Forest[J]. Ecology and Environment, 2022, 31(1): 17-25.

殷祚云. 南亚热带森林3层次物种多度之广义泊松分布模型[J]. 生态环境学报, 2022, 31(1): 17-25.

Figures/Tables 4

Table 1 The descriptive statistics of species abundances in the tree, shrub and herb layers of evergreen needle- and broad-leaved mixed forest community in Dinghushan Biosphere Reserve, South China

Layer	Area/m²	S	N	Min	Max	Median	Mode	m	v	v/m ratio	D_sw	E_sw
Tree	10000	69	3890	1	772	3	1	56.38	19317.30	342.65	3.923	0.642
Shrub	625	39	428	1	83	3	1	10.97	340.97	31.07	4.010	0.759
Herb	25	32	151	1	29	2	1	4.72	35.24	7.47	4.207	0.841

Figure 1 Comparisons of the zero-truncated generalized Poisson (GP) distributions fitted to the SAD data among the tree, shrub, and herb layers of evergreen needle- and broad-leaved mixed forest community in Dinghushan Biosphere Reserve, South China

Table 2 Fitting results of the zero-truncated generalized Poisson (GP) distributions to the species abundance distributions (SADs) in the tree, shrub, and herb layers of evergreen needle-and broad-leaved mixed forest community in Dinghushan Biosphere Reserve, South China

Layer	λ	α	P(χ²)	P₀	S^*	M'	V'	S^*(α)
Tree	27.345	1.470	0.395	0.515	142.3	56.38	94073.15	139.8
Shrub	4.908	1.483	0.160	0.553	87.2	10.97	685.64	79.5
Herb	1.676	1.682	0.066	0.645	90.1	4.72	54.49	71.4

Table 3 Comparisons of the goodness of fit between the generalized Poisson (GP) and Poisson lognormal (PLN) distributions in describing the species abundance distributions (SADs) of the tree, shrub, and herb layers of evergreen needle- and broad-leaved mixed forest community in Dinghushan Biosphere Reserve, South China

Layer	GP			PLN
Layer	lnL	AIC	CAIC	lnL	AIC	CAIC
Tree	-265.3	267.3	541.0	-930.7	932.7	1876.0
Shrub	-116.9	118.9	243.1	-117.5	119.5	247.9
Herb	-74.0	76.0	157.0	-74.7	76.7	161.4

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Using Generalized Poisson Distribution to Model the Patterns of Species Abundances in Three Layers of South Subtropical Forest

南亚热带森林3层次物种多度之广义泊松分布模型

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